Red Canners

There are three options in the case on which a decision needs to be made
1) What grade of tomatoes should be used to make what type of product in the existing scenario?
2) Should the company purchase additional tomatoes?
3) Should the company consider Myers costing methods

First Option:

Firstly, we will calculate the product mix used to make different type of products in the existing scenario to maximize profit.

Decision Variables:
Let AW be the pounds of “Canned Whole Tomatoes” produced using Grade A tomatoes.
Let AJ be the pounds of “Tomato Juice” produced using Grade A tomatoes.
Let AP be the pounds of “Tomato Paste” produced using Grade A tomatoes.
Let BW be the pounds of “Canned Whole Tomatoes” produced using Grade B tomatoes.
Let BJ be the pounds of “Tomato Juice” produced using Grade B tomatoes.
Let BP be the pounds of “Tomato Paste” produced using Grade B tomatoes.

Objective Function:
Max, Z = 1.48/18(AW+BW) +1.32/20(AJ+BJ)+1.85/25(AP+BP) – 180000
i.e Z= 0.08222(AW+BW) + 0.066(AJ+BJ) + 0.074 (AP+BP) – 180000
Subject To:

Demand Constraints:
Whole tomatoes, AW + BW ≤ 14400000
Tomato Juice, AJ + BJ ≤ 1000000
Tomato Paste, AP + BP ≤ 2000000

Quality Constraints:
For Canned whole tomatoes, (0.9AW + 0.5BW)/2 ≥ 0.8 (AW + BW)/2
For Tomato Juice, (0.9AJ + 0.5BJ)/2 ≥ 0.6 (AJ + BJ)/2

Quantity Constraints:
AW + AJ + AP ≤ 600000
BW + BJ + BP ≤ 2400000

Non-Negativity Constraints:
AW, AJ, AP, BW, BJ, BP ≥ 0

Sensitivity Report:

Hence, the Total Profit from using the following product mix in the products;

AW = 52500
AJ = 75000
AP = 0
BW = 175000
BJ = 225000
BP = 2000000

Net Profit = 45354 -------------------- (1)

Second Option:

Now, the second option where the company might decide to buy 80000 more Grade A tomatoes, then the Profit would be as follows;

Decision Variables:
Let AW be the pounds of “Canned Whole Tomatoes” produced using Grade A tomatoes.
Let AJ be the